To solve the logarithmic equation:

$\log_8(s) = -6$

Step 1: Rewrite the logarithmic equation in exponential form.

The logarithmic form $\log_b(a) = c$ can be rewritten as: $b^c = a$

For this problem: $\log_8(s) = -6 \implies 8^{-6} = s$

Step 2: Calculate $8^{-6}$.

$8^{-6} = \frac{1}{8^6}$

Now, find $8^6$: $8^6 = 262144$

So, $s$ becomes: $s = \frac{1}{262144}$

Final Answer:

$s = \frac{1}{262144}$

Would you like more details or have any questions?

Related Questions:

1. How do you convert a logarithmic equation to exponential form?
2. What is the general process for solving equations involving logarithms?
3. How do negative exponents affect the values of numbers?
4. How can logarithmic equations be used in real-world applications?
5. What are the properties of logarithms that simplify solving such equations?

Tip:

When solving logarithmic equations, always remember that $\log_b(a) = c$ can be rewritten as $b^c = a$. This conversion is often the key to finding solutions.